Contribution of Leningrad scientists to the development of control systems sensitivity theory

Abstract

ленинградских ученых в развитие теории чувствительности систем управления. Аннотация. Теория чувствительности объединяет принципы и методы исследования влияния вариации параметров на свойства систем управления. Как самостоятельное научное направление теория чувствительности начала формироваться в конце пятидесятых и начале шестидесятых годов двадцатого столетия. На ее становление заметное влияние оказали работы ленинградских ученых Розенвассера Е.Н. и Юсупова Р.М. В статье приводятся общие сведения об истории развития теории чувствительности, о вкладе авторов в ее формирование в рамках теории управления и общей теории динамических систем, о той научно-организационной деятельности, которая проводилась в стране, в том числе с участием авторов, по продвижению теории чувствительности. Ключевые слова: теория чувствительности, вариация параметров, дополнительное движение, функции и коэффициенты чувствительности, уравнения чувствительности. Rozenwasser E.N., Yusupov R.M. Contribution of Leningrad scientists to the development of control systems sensitivity theory. Abstract. The sensitivity theory combines the principles and methods for exploring the influence of parameters variation on properties of control systems. The sensitivity theory was formed at the end 1950s-the beginning of 1960s as an independent scientific field. Rozenwasser E.N. and Yusupov R. M. made a significant contribution to its formation. The paper describes general aspects of the historical development of sensitivity theory, the authors' contribution to its formation within the control theory and the general theory of dynamic systems, and scientific and organizational activity which was carried out in the country with participation of authors on promotion of the sensitivity theory.

Method of successive approximation in mathematical modelling of geotechnical mechanics problems

“…Product functions in the multiplicative form of representation are found in the class of elementary functions. One of the advantages of the multiplicative form of the mathematical model (MM) representation is that by using power functions of the product, it is possible to make an approximate estimate of the function sensitivity to the variation of parameters of the problem [4], [5]. In these cases, the use of the SAM method makes it possible to significantly reduce time costs and obtain a result in analytical form as a product of elementary functions and parameters.…”

“…Instead of using the TS to determine the sensitivity in technical applications, it is proposed to use the approximation of the function itself, but in some set of points in the domain of definition. Since it is proposed to approximate the function in the form of a product of power functions, each of which depends on only one parameter [5], the sensitivity to the parameter variation can be approximately determined by the power indicators [4]. The higher is the power indicator, the greater is the influence of this parameter on the function.…”